The striker is under contract at the Stadium of Light until the summer of 2023 following his move from Ross County in January 2021.
Back in August, Rangers were reportedly told they that could be forced to stump up £5million to land Stewart.
However, that valuation may well have increased following Sunderland’s promotion to the Championship.
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According to fresh reports from The Mirror, Rangers still want to sign Stewart despite Sunderland’s promotion.
They also state that Middlesbrough, QPR and Sheffield United are also in the hunt to sign the 25-year-old.
Stewart notched his 26th goal of the season during the League One play-off final win over Wycombe Wanderers at Wembley.
The Mirror also states that Sunderland are keen to tie Stewart down to a new lucrative deal that will make him the best-paid player at the club.